Quite apart from the general notion of polishing as a means for enhancing the beauty of an object, polishing operations are also used in a variety of industrial fabrication processes. The fabrication of semiconductor integrated circuits and the fabrication of optical surfaces are good examples where polishing operations are required to enhance the functionality of the finished product.
As is well known, semiconductor integrated circuits are fabricated on a silicon wafer in multiple layers using plasma assisted deposition/etching processes. Typically, after each layer has been fabricated, the surface of the top layer is polished flat so that the next layer can be fabricated without interference from preexisting surface irregularities. Plasma assisted etchback and chemical mechanical polishing (CMP) are two processes which have been previously employed for this purpose. It is known, however, that, the etchback process cannot make a surface truly flat. This is because etchback processes tend to take off the same amount of material equally over the entire surface of the material; without regard to the surface contour of the material. Consequently, the more pronounced surface irregularities are not removed.
Although for some applications CMP may be more effective than plasma assisted etchback, the CMP process requires the use of a separate environment from the one used for the plasma assisted deposition/etching process. As a result, CMP is a time consuming process due to the fact there is a need to change environments for each polishing of the substrate. Furthermore, an inability to measure the progress of CMP polishing makes CMP a generally hit and miss operation. Also, the mechanical polishing of a surface with abrasives does not result in a very smooth surface finish, and any contamination of the surface caused by abrasive materials or chemicals used for polishing is an important concern.
In a departure from known polishing processes the present invention recognizes that plasmas can be created and controlled to perform a polishing action that is separate and distinct from the now familiar deposition and etching operations. In the present invention, the plasma ions are accelerated and made to impact the substrate at a grazing angle. The sputtering, due to the ion impact at a grazing angle, removes the substrate atoms preferentially from protruding surface morphology and thus polishes the surface. To appreciate this departure, some technical information is helpful. Specifically, it is helpful to consider a sputtering process in which atoms are removed from a surface by the bombardment of positive ions, and the effect which a magnetic field can have on directing the acceleration of ions into collision with the surface.
It is well known that the sputtering yields of ions depend on both their mass and their energy. It is also known that variations in a sputtering process due to changes in the substrate materials are minor. Insofar as the mass of the ions are concerned, the yields from ions of the heavier noble gases, such as Ne, Ar, Kr and Xe, are practically the same at any given energy. It turns out, however, that the sputtering yields of lighter ions, such as He and H, are at least one order of magnitude smaller than those of the heavier ions. Accordingly, for purposes of the present invention, the sputtering yields of these lighter ions are onsidered negligible.
Insofar as the energy level of ions in a sputtering operation is concerned, it happens that once the ion energy level is above a threshold energy W.sub.c (W.sub.c is approximately 30 eV), the sputtering yield increases rapidly with further increases in the ion energy W. After a rather rapid increase, the sputtering yield plateaus around 10 keV. For the energy range of interest for the present invention, e.g. 30 eV-300 eV, the experimental data of the sputtering yield, Y, of the heavier ions can be fitted with a formula given by: EQU Y={W[eV]-W.sub.c [eV]}/270 eV [1]
As shown by formula [1], the yield reaches unity around an ion energy of 300 eV.
Unlike other sputtering processes, the present invention requires that ions move along predetermined paths, or trajectories. To do this, the present invention makes use of the fact that any particle of charge e moving with a velocity v perpendicular to a magnetic field of flux density B, moves in a circular path. Thus, for a uniform magnetic field of substantially constant field strength B in the z-direction, the motion of an ion in the x-y plane under the influence of an r-f electric field E is given by the formula: EQU E.sub.y =E cos [.OMEGA.t+.phi.] [2]
Where: EQU .OMEGA.=eB/M [b 3]
In formulae [2] and [3], .phi. is the phase of the r-f electric field at t=0, and .OMEGA. is the cyclotron angular frequency which is equal to 2 .pi. times the number of revolutions an ion makes around the z-directed path per second. M is the mass of the ion.
The equations of motion of an ion with mass M are then given by the expressions: EQU Mdv.sub.x /dt=ev.sub.y B EQU Mdv.sub.y /dt=eE.sub.y -ev.sub.x B [4]
Initially, as an ion is created from a gas atom by ionization, its velocity is negligibly small. Accordingly, we can assume that the velocity is zero at t=0. From this initial condition, when the ion is accelerated by an r-f signal, we obtain EQU v.sub.x =[eEt/2M]sin [.OMEGA.t+.phi.]-[eE/2M.OMEGA.]sin .phi.sin .OMEGA.t EQU v.sub.y =[eEt/2M]cos [.OMEGA.t+.phi.]+[eE/2M.OMEGA.]cos .phi.sin .OMEGA.t[5 ]
After a few cycles the second terms become small compared to the first terms and the velocities are approximately equal to EQU v.sub.x .congruent.[eEt/2M]sin [.OMEGA.t+.phi.] EQU v.sub.y .congruent.[eEt/2M]cos [.OMEGA.t+.phi.] [6]
From these equation it can be appreciated that the ion is a spiral in which both the magnitude of the velocity v and the gyro-radius .rho. of the ion increase linearly with time. These variables are calculated with the following formulas: EQU v=[eEt/2M] EQU .rho.=[Et/2B] [7]
Because the ions are accelerated along an outwardly expanding spiral path, if two plates are placed at y=0 and y=h, the ions are lost when their orbits intersect either of these plates. The ions born between y=0 and y=h/2 reach the bottom plates and the ions born between y=h/2 and y=h reach the top plate. The ions produced at y=y.sub.o reach the plate in the period .tau. given by ##EQU1##
Depending on where they are born, the velocity of the ions as they strike the plates will range from 0 to v.sub.m =.OMEGA.h/2, and their energy will vary from 0 to a value for W.sub.m =e.sup.2 B.sup.2 h.sup.2 /[8M].
Using the sputtering yield as a function of the energy (see [1] above) the average yield &lt;Y&gt; is calculated with the expression: EQU &lt;Y&gt;=.intg.Ydv/v.sub.m [ 9]
From this we obtain: EQU &lt;Y&gt;=[1/3][W.sub.m +.sqroot.W.sub.m W.sub.c -2W.sub.c ][1-W.sub.c /W.sub.m ]/270 eV [10]
For example, if W.sub.m =300 eV and Wc=3-eV the average yield is 0.37.
As the orbiting ions approach the substrate surface, the closest point in their respective trajectories move closer to the substrate surface in steps. During each cyclotron cycle the gyroradius increases by .DELTA..rho. which is given by the equation: EQU .DELTA..rho.=[.pi.E/B.OMEGA.] [11]
Due to the increasing .DELTA..rho., depending on where the ion is born, the ion impact angle (.theta.) will vary. In this context, .theta. is the angle between the path of the ion and the surface of the substrate. For example, if the closest point in the ion path is just .DELTA..rho. away from the surface on a particular pass, the ion will strike the surface tangentially on the next pass. On the other hand, if the orbiting ion just misses the surface on a pass the ion will intersect the surface with the maximum angle .theta. on the next pass. The range of the angle .theta. between the direction of the ion motion at the impact and the surface is given by the expression: EQU 1&gt;cos .theta.&gt;[1+.DELTA..rho./.rho.].sup.-1 [ 12]
By assuming .theta. is small, we obtain the expression: EQU 0&lt;.theta..sup.2 &lt;2.DELTA..rho./.rho. [13]
For ions having maximum energy, equation [13] becomes: EQU 0&lt;.theta..sup.2 &lt;[4 .pi.E/B.OMEGA.h] [14]
For example, with B=0.3T, .OMEGA.-7.5.times.10.sup.5 sec.sup.-1, h=0.1 m and E=200 V/m the angle ranges between 0 and 19 degrees.
So far we have assumed that the frequency for accelerating the ions is the frequency required for ion cyclotron resonance heating (ICRH). Also, it has been assumed that this frequency is maintained exactly equal to the cyclotron frequency of the ions. It happens, however, that when the frequency of the r-f excitation is slightly detuned, or moved off resonance, the phase of the ion orbits will slip with each succeeding cycle. As the phase slips, the velocity of the ions initially increases. Then after enough phase slippage has accumulated, the velocity decreases. It turns out there are advantages to be gained by employing the slightly detuned r-f frequency. Primarily, by using detuning techniques, the acceleration rate of the ions can be reduced as their orbits come close to the plates. This reduced acceleration translates into a reduced angle .theta. at the point of impact.
For purposes of the present invention, the ICRH field can be determined with the following formula: EQU E.sub.y =E cos [.omega.t+.phi.] [15]
In formula [15], .omega. is the r-f angular frequency. When the r-f angular frequency is off resonance by .DELTA..omega., the expression is: EQU .omega.=.OMEGA.+.DELTA..omega. [16]
With an off-resonance r-f angular frequency, the velocities of the ion are given by the expressions: ##EQU2## By ignoring small terms in the expression [17] we obtain: EQU v.sub.x .congruent.[eE/M.DELTA..omega.]sin [.OMEGA.t+.DELTA..omega.t/2+.phi.]sin [.DELTA..omega.t/2] EQU v.sub.y .congruent.[eE/M.DELTA..omega.]cos [.OMEGA.t+.DELTA..omega..phi.t/2+]sin [.DELTA..omega.t/2] [18]
From the above expressions [18] it can be seen that the magnitude of the velocity oscillates and does not increase indefinitely. This is unlike the case where .DELTA..omega.=0.
When using the above expressions for the velocities of the ions, and under the condition where .DELTA..omega..apprxeq.0, the gyro-radius and its rate of increase becomes EQU .rho.=[E/B.DELTA..omega.]sin [.DELTA..omega.t/2] EQU d.rho./dt=[E/2B]cos [.DELTA..omega.t/2] [19]
It can be noted that at the limit of .DELTA..omega.=0, the above equations are identical to eq[5], eq[6] and eq[7]. With this in mind, the condition that all the ions reach the plates is given by: EQU .DELTA..omega.&lt;[hB/2E] [20]
The increase of the gyro-radius in one cycle and the range of the impact angle are respectively given by the expressions: EQU .DELTA..rho./.rho.=.pi.{[E/Bv].sup.2 -[.DELTA..omega./.OMEGA.].sup.2 }.sup.1/2 [ 21] EQU 0&lt;.theta..sup.2 &lt;2 .pi.{[E/Bv].sup.2 -[.DELTA..omega./.OMEGA.].sup.2 }.sup.1/2 [ 22]
Upon comparing the above expressions with eq [11] and eq [12], it will be appreciated that an appropriate amount of detuning can be effective in reducing the angle of impact .theta.. As contemplated for the present invention, the detuning is accomplished by changing either the frequency of the r-f electric field or the strength of the magnetic field.
Because ICRH increases only the perpendicular velocity of the ions (i.e. velocity components in the x-y plane), the ions move along the magnetic field lines in the z direction at their thermal velocity v.sub.th. The condition that the ions strike the substrate before leaving the region in the z-direction is given by the following formula: EQU .tau.&lt;L.sub.z /[2V.sub.th ] [23]
where L.sub.z is the length of the region in z-direction. By using eq [8] given above, we obtain: EQU E&gt;[hB/L.sub.z ][2kT/M] [24]
where T is the gas temperature. For example with h=0.1 m, B=0.3T, T=500.degree. K. and argon gas, the above condition becomes E&gt;45 V/m.
A concern for the accelerated ions is that they may collide with gas atoms during their acceleration. If this happens, the collisions will destroy the synchronism between the ion orbits and the r-f field. These collisions may also change the angle .theta. at which the ions impact on the plates. Therefore, it is important to accelerate the ions at a rate which will avoid the collisions. The rate at which the ions can be accelerated and reach the substrate without suffering the collisions is given by the following formula EQU n.sub.o .sigma..sub.1 W/(eE)&lt;1 [25]
where n.sub.o is the density of gas atoms and .sigma..sub.1 is the collision cross-section. For example, .sigma..sub.1 =6.times.10.sup.-20 m.sup.2, W=300 eV and E=200 V/m results in n.sub.o &lt;1.1.times.10.sup.19 m.sup.-3 13=3.times.10.sup.-4 Torr.
Thus far we have considered the acceleration of ions in a magnetic field due to ICRH. For the present invention, however, not all ions in the plasma are to be accelerated by ICRH. Instead, only ions from a minority gas in a gas mixture are to be so accelerated. The plasma ions are a mixture of the majority ions and the minority ions. The minority ions will be from a different gas than the majority ions, and both will be generated by a process which is commonly known as electron cyclotron heating (ECH).
Plasma production by ECH is well known. Typically, for ECH, a microwave is radiated into a gas or gas mixture which is contained within a vessel chamber. This can be done with antennas having multiple slots. With this radiation, electrons are heated by electron cyclotron resonance. Gas atoms are then ionized by the electrons and the resultant plasma is maintained in the vessel chamber by ECH power. Because of its high efficiency ECH is known to be capable of maintaining plasmas at a low neutral gas pressure. In the particular geometry envisioned for the present invention, due to the presence and orientation of the magnetic field, the plates which hold the substrates are magnetically insulated from the plasma, and the main plasma loss is to the vessel walls along the magnetic field lines. Under these conditions, the required ECH power P.sub.ec to balance the plasma loss to the walls is given by the expression: EQU P.sub.ec =1.2.times.L.sub.z hn.sub.e [T.sub.e /M.sub.i ].sup.1/2 Q.sub.i[ 26]
where L.sub.z is the length of the plasma in the x-direction, n.sub.e is the electron density, t.sub.e is the electron temperature, M.sub.i is the mass of the majority ions and Q.sub.i is the energy required to ionize the atom including the excitation loss prior to the ionization. For helium plasma with T.sub.e =5 eV, Q.sub.i =80 eV, L.sub.z =0.4 m and H=0.1 m the expression [26] becomes: EQU P.sub.ec =6.8.times.10.sup.-15 n.sub.e [ 27]
To achieve the density of 10.sup.17 m.sup.-3, the required power is 680 watt.
As mentioned above, Ion cyclotron resonance heating (ICRH) is a mode for heating a plasma by resonant absorption of energy based on the waves inducted in the plasma at the cyclotron frequency of the ions. Because the ICRH frequency of the minority ions is lower than the cyclotron frequencies of both the electrons and the majority ions, the plasma oscillates in the x-direction in response to the ICRH field in the y-direction. The velocity of this oscillation u.sub.x is given by EQU u.sub.x =E.sub.y /B=[E/B]cos [.OMEGA.t+.phi.] [28]
Because of their non-negligible mass, the majority ions move in the y-direction at the velocity u.sub.y given by EQU u.sub.y =[-.OMEGA./.OMEGA..sub.i ]E sin [.OMEGA.t+.phi.] [29]
where .OMEGA..sub.i is the angular cyclotron frequency of the majority ions. This response is out of phase with respect to the field and is, therefore, capacitive. In this case the capacitance C of the plasma is given by the expression: EQU C=[nM.sub.i /B.sup.2 ][L.sub.x L.sub.z /h] [30]
where M.sub.i is the mass of the majority ions. The capacitive impedance Z.sub.c thus becomes EQU Z.sub.c =[M/M.sub.i ][B/en][h/L.sub.x L.sub.z ] [31]
For example, M/M.sub.i =10, B=0.3 T, n=10.sup.17 m.sup.-3, h=0.1 m and L.sub.x =L.sub.z =0.3 m, the impedance is 200.OMEGA..
It happens that the minority ions in the plasma respond quite differently to the ICRH field than do the majority ions. Specifically, at cyclotron resonance, the reactive part of the response of the minority ions vanishes and the response is determined by the dissipation which results from ion collisions with the gas atoms or the plates. Stated differently, the accelerated ions will reach the substrates that are mounted on the plates before they suffer collisions with gas atoms in the plasma. Therefore, the effective collision time .tau..sub.c is determined by the time it takes for the ions to reach the substrates. This time depends on the position y of the particular ion and its velocity v. The effective collision time is given by the expression: EQU .tau..sub.c [v,y]=[2By/E][1-v/v.sub.m ] [32]
Thus, the ions with larger velocities contribute more to the current but the effective collision time is shorter. The average effective collision time &lt;.tau..sub.c &gt; weighted by the velocity is given by the expression: EQU &lt;.tau..sub.c &gt;=By/[3E] [33]
Based on expression [33] the current in y-direction is given by; EQU j.sub.y =[e.sup.2 n By/3M]cos [.OMEGA.t+.phi.] [34]
The power dissipation per unit volume is given by; EQU E.sub.y j.sub.y =[e.sup.2 nBEy/6M] [35]
and, the total power P.sub.Ic becomes; EQU P.sub.Ic =e.sup.2 nBEh.sup.2 L.sub.x L.sub.z /[24M] [36]
It is to be appreciated that the total power, P.sub.Ic, must be equal to the power deposited on the plates by the minority ions. The total flux .GAMMA. of the minority ions to the plates is calculated by the formula: EQU .GAMMA.=nEL.sub.x L.sub.z /B [37]
and the average energy &lt;W&gt; of the ions at the impact is; EQU &lt;W&gt;=e.sup.2 B.sup.2 h.sup.2 /[24M] [38]
The product of the flux .GAMMA. and the average energy &lt;W&gt; is equal to the ICRH power P.sub.Ic. For example, with B=0.3 T, L.sub.x =L.sub.z 0.3 m, h=0.1 m, n=10.sup.16 m.sup.-3, E=200 V/m and argon ions, the flux is 6.times.10.sup.17 /sec and the power is 86 watt.
The current in the y-direction, J.sub.y (see [34] above), is non-uniform and induces the current in the direction of the magnetic field carried by the electrons to keep the current divergence free. The current density in the z-direction at the walls is given by EQU J.sub.z =.+-.[e.sup.2 nBL.sub.z /6M]cos [.OMEGA.t+.phi.] [39]
where the negative sign applies for 0&lt;y&lt;h/2 and the positive sign applies for h/2&lt;y&lt;h.
Because of the flux of the minority ions to the plates, there is a net loss of the ions from plasma. Thus, in order to keep the charge balance in the plasma, electrons must leave the plasma parallel to the magnetic field and add an additional current with a d.c. component which corresponds to the total flux .GAMMA. of the minority ion flux to the plates.
With the technical aspects of the present invention set forth above in mind, and in light of the difficulties presently encountered by alternative polishing methods mentioned above, it is an object of the present invention to provide a grazing angle plasma polisher which uses the same environment for both polishing and for a plasma assisted deposition/etching operation. It is another object of the present invention to provide a grazing angle plasma polisher which uses optical measurements for feed back control over the depth and smoothness of the polishing operation. Still another object of the present invention is to provide a grazing angle plasma polisher which can simultaneously polish a plurality of substrate surfaces. Yet another object of the present invention is to provide a grazing angle plasma polisher which is relatively easy to manufacture, operationally simple to use, and comparatively cost effective.